Monday, August 29, 2011

Most universities now have various procedures that graduate students have to complete to continue with their research degree. At UQ there are three milestones: confimation, mid-candidature review, and thesis review.

I consider that the more rigorous, organised, and disciplined the process, the more helpful it is for the candidate and the more effective it is at preventing problems.

By far the most important milestone is confirmation of candidature after one year of enrolment. It should include writing a literature review, giving a seminar, an interview with the confirmation committee, and written feedback to the candidate from the committee. It is important that this stage is implemented with rigorous deadlines. Otherwise things can get drawn out, students coast, and problems get even worse. The student should go thru the process within 12 months (for full-time students). Weak students may be given a 6 month extension with specific goals to meet. If they do not, their candidature should be terminated. This difficult step can save everyone concerned a lot of wasted time if an unsuitable student is allowed to continue.

Saturday, August 27, 2011

It is well established that in superfluid 3He that the Cooper pairs are in a spin triplet state. It is believed that this results from ferromagnetic spin fluctuations within the normal Fermi liquid state.

It remains to be established whether there are any superconductors in a spin triplet state. The most promising candidates are Strontium Ruthenate (Sr2RuO4) [see this review by Andy Mackenzie and Yoshi Maeno] and the Bechgaard salts (TMTSF)2X [see this PRB].

I assumed that a necessary ingredient for triplet superconductivity would be Cooper pairing via exchange of ferromagnetic spin fluctuations. However, I learnt this week that this is not the case. It seems that in quasi-one-dimensional quarter-filled bands (as in the Bechgaard salts) charge fluctuations and the associated competition between CDW and SDW order can lead to an associated competition between spin triplet "f-wave" pairing and spin singlet "d-wave" pairing. The figure below shows that associated signs of the order parameter over the first Brilloiun zone and Fermi surface.

[The figure is taken from a paper by Kuroki and Tanaka]. Note that the variation in the magnitude of the order parameter over different parts of the Fermi surface is the same for both. Just the sign is different on the two Fermi surface sheets. Hence, it is conceivable that a particular pairing interaction should lead to these two states being competitive with one another.

This PRL provides a renormalisation group analysis which illustrates this competition and highlights the importance of reducing the Fermi surface nesting to produce the triplet state. A recent PRL suggests similar considerations may actually also apply to strontium ruthenate.

I thank Nigel Hussey and Jaime Merino for introducing me to the literature.

Thursday, August 25, 2011

Quantum entanglement is required for various "useful" quantum information processing tasks such a teleportation, dense coding, and quantum key distribution.
How crucial entanglement is for actual quantum computation turns out to be a subject of debate. For mixed states the presence of entanglement is a necessary but not a sufficient condition to violate Bell inequalities, as found in a classic paper by Werner.

In practice, if one builds some quantum information processing device in the laboratory one will never create maximal entanglement between qubits. For example, in a quantum dot computer the spin singlet-triplet splitting is switched on and off in order to swap electronic spins. But, the possibility of electronic double occupancy can reduce this entanglement, but not fatally, as discussed here.

So can we quantify how much entanglement is enough to be useful? Is there a lower bound on how much entanglement a gate must create to be useful? Is there some rough figure of merit?
I cannot find any discussion of this basic question in the literature. I scanned through the nice Reviews of Modern Physics article by Horodecki^4 but could not find anything.

Any ideas?

The above question was raised by one of the referees for a recent paper (with Laura McKemmish, Noel Hush, and Jeff Reimers) where we calculate the entanglement between the electronic and nuclear degrees of freedom in the low lying eigenstates of a model Hamiltonian for several simple molecules.

Wednesday, August 24, 2011

The paper Consistent description of the metallic phase of overdoped cuprate superconductors as an anisotropic marginal Fermi liquid that Jure Kokalj and I recently wrote has just been accepted for publication in Physical Review Letters.We received two very detailed and helpful referee reports which led us to significantly improve the manuscript. Here I mention just one point. Both referees were surprised that we showed clear disagreement between the temperature dependence of the anisotropic scattering rate and the Hidden Fermi liquid theory of Casey and Anderson [which showed agreement in a recent PRL]. Both referees suggested that it was the manner in which we did our plots, which was different from Casey and Anderson. So we produced the plot below. The key difference is that we used a much larger vertical scale and we compared data at several different dopings.

Tuesday, August 23, 2011

Water is everywhere, even in the air. Consequently, many surfaces (metallic, oxide, and semiconducting) are covered in thin layers of water. It turns out that the first contact layer is actually not pure water, but a mixture of water and hydroxyl (OH-) ions. Furthermore, on a metal surface the separation of the oxygen atoms is largely determined by the lattice constant of substrate [presumably because the oxygen atom lone pairs have a relatively strong interaction with the metal atoms].

On some metals the oxygen atoms are close enough (as in ice under high pressures) that the hydrogen bond between water and hydroxyl ion takes on a covalent character and there is significant delocalisation of the shared proton between the two oxygen atoms.

The comparison between present results and the reported experimental findings is difficult. It seems to be clear, though, that site correlations do not play a role at physiological conditions and that the biological function of the FMO complex is not affected by spatial site energy correlations. A similar conclusion has already been drawn for the light-harvesting II complex of Rhodospirillum molischianum in a similar study.

Friday, August 19, 2011

the one-electron Green function has a simple pole in the complex energy plane. The strength of this pole is the quasi-particle weight Z.

The second is the more fundamental because it is connected with the existence of quasi-particles.

There are now a diverse range of strongly correlated electron materials which do not have the first signature. In particular, many have a resistivity which is linear in temperature over a wide temperature range. However, this does not necessarily imply the absence of quasi-particles. For an illustration of some of the subtleties involved see this post.
In marginal Fermi liquid theory the scattering rate is linear in temperature but there is a non-zero quasi-particle weight, except at zero temperature.

As discussed in another post, Jan Zaanen claims that when the scattering rate (hbar/tau) has magnitude k_B T, one reaches the "Planckian limit" and there are no quasi-particles. It is not clear to me what is the basis of this claim. I welcome comments.

They do a Compton scattering experiment (X-rays are inelastically scattered of the electrons) on an ice crystal. The paragraph below explains the basic physics.

The key figure in the paper is below. The red dots show the measured difference between the momentum dependence of the Compton scattering in different directions. The solid curve is the prediction of a band structure calculation which implicitly assumes complete quantum coherence (i.e. covalency). In contrast an electrostatic model (with no quantum coherence) gives the dot-dashed line which exhibits little anisotropy. The peaks in the inset at 1.7 and 2.85 Angstroms correspond to the H bond length and shortest Oxygen-Oxygen distance.

Aside. With regard to the solid curve above, the authors state, "There are no adjustable parameters in the theory except that a 40% reduction of the theory is required". Sounds like one adjustable parameter, to me!

Monday, August 15, 2011

A key aspect of science is comparing your results with those of earlier work. This may seem basic but people do not do it as much as they should. For example, theorists should be comparing their results to actual experimental data.

But this post is just concerned with the mundane practicalities. In the "old days" one would ask experimentalists to send an electronic version of the data. Now it is possible to just extract the data from figures in papers.

A relatively easy way is using DataThief. Last week I downloaded it and found within 2 hours I had figured out how to use it and could produce graphs with my theoretical curves compared to the experimental data.

Saturday, August 13, 2011

There is an interesting (and depressing and challenging) Perspective, The Gratzel cell: Where next?, by Laurence Peter in Journal of Physical Chemistry Letters. Here is the beginning of the abstract:

Twenty years after O’Regan and Grtzel’s seminal Nature paper entitled “A Low-Cost, High-Efficiency Solar-Cell Based on Dye-Sensitized Colloidal TiO2 Films”, dye-sensitized solar cells (DSCs) and analogous devices have become a major topic of research, with over 1000 papers published in 2010. Although much more is now known about the physical and chemical processes taking place during operation of the DSC, the exponential increase in research effort during this period has not been matched by large increases in efficiency.

The paper gives a nice summary of some of the key scientific challenges. I thank Seth Olsen for bringing the paper to my attention.

The figure below is a helpful summary of the main results. The colour shading shows the quasi-particle weight Z in the metallic phase as a function of U/D and band filling for a system with 3 degenerate bands for a fixed value of J=0.15U. [The relevant multi-band Hubbard model is solved at the level of Dynamical Mean-Field Theory (DMFT)]. The cases n=2 and 4 are particularly interesting because there is a large range of U/D for which one has a metallic phase with small Z. The authors characterise this as a bad metal (i.e. which occurs above some relatively low coherence temperature T*).

One minor comment. The authors mention just a few signatures of bad metals [large resistivity above the Mott-Ioffe-Regel limit and large poorly screened local moment]. Others include no Drude peak in the optical conductivity, and a large thermopower ~k_B/e [see this earlier post].

So what is this about Janus faced? I had no idea. But I found out that Janus was a Roman God of transitions. He looked to the past and future and was often depicted in statues as "two-faced". The point here is that Hund's rule can either enhance or reduce the correlations, depending on the filling.

I thank Jaime Merino for bringing the paper to my attention and for some helpful discussions about it.

These results should provide significant constraints on molecular dynamics simulations on such systems.

Also, this seems a more straightforward approach to investigating ion channels than a recent proposal to use quantum decoherence of NV diamond centres to detect the very small magnetic fields associated with the electrical currents in ion channels. But, I am probably missing something.

Tuesday, August 9, 2011

Charles Coulson is one of my scientific heroes. I love his book Valence, which help shape the development of quantum chemistry. With Danielsson he published two often cited papers on a valence bond theory of the hydrogen bond in 1954. But they are in a now defunct journal Akiv fur Fysik, published by the Swedish Academy of Sciences from 1949 to 1974. I could not find the article online by managing to get a copy from the Warehouse of the UQ library. So I post a copy here in case others would like to read this classic paper. Just the conclusion is worth reading.

One minor comment. The authors consider a basis of 3 valence bond states. Two of these involve the ionic and covalent components of an O-H bond in the donor molecule. Hence, it may be possible to combine these both into a single diabatic state describing the full O-H bond. I think this is essentially what is done in Warshel's empirical valence bond theory of proton transfer reactions.

Trivial aside: Danielsson's address is Swedish Cement and Concrete Research Institute! But, the article says they did the work at Kings College London.

Monday, August 8, 2011

Last week there was an interesting paper in Nature Link between spin fluctuations and electron pairing in copper oxide superconductors
Most high-Tc cuprate superconductors are hole doped. However, the past decade has seen studies of electron doped cuprates which have some similarities but also some significant qualitative differences. Thus there is electron-hole asymmetry.
In particular there appears to be no pseudogap in the electron-doped materials and they are not as strongly correlated.

The authors measured the temperature and doping dependence of the intralayer resistivity and deduced the phase diagram below.

Specifically, they found that for dopings x less than approx. 0.17 they could fit the resistivity to a linear in T form over 3 decades of temperature. As x decreased the co-efficient of proportionality increased roughly proportional to Tc.
For x larger than 0.17 there is no superconductivity and the resistivity could be fit to a quadratic T dependence, characteristic of Fermi liquid theory. The coefficient of proportionality becomes larger as x=0.17 is approached.

The authors note similar behaviour is seen in the Bechgaard salt (TMTSF)2PF6.

Later I will compare the above behaviour to what happens in the hole-doped cuprates, reported in a 2009 Science paper.

If one sticks with a one band Hubbard or t-J model and a band structure with next-nearest neighbour hopping t' [which produces electron-hole asymmetry] can one reproduce the key aspects of the electron-hole asymmetry in the phase diagram?
Maybe. But if one looks at the underlying electronic structure the electron and hole doped materials are different, according to this recent Nature Physics paper.

The use of Empirical Valence Bond methods to describe chemical reactions in complex environments (e.g. solvents and proteins) was pioneered by Warshel. I found the useful table below in a Comment by Jan Florian, arguing that some "new" methods with new acronyms are actually misnomers. [Aside: this is the same issue as The Best Paper Title and Abstract Ever].

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About Me

I have fun at work trying to use quantum many-body theory to understand electronic properties of complex materials.
I am married to the lovely Robin and have two adult children and a dog, Priya (in the photo). I also write an even more personal blog Soli Deo Gloria [thoughts on theology, science, and culture]

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